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We have derived the bivariate luminosity function for the far-ultraviolet (1530 Å) and far-infrared (60 μm). We use matched GALEX and IRAS data, and redshifts from NED and the PSCz survey. We have derived a total star formation luminosity function ϕ (L tot), with L tot= L FUV+ L FIR. Using these, we determined the cosmic" star formation rate"(SFR) function and density for the local universe. The total SFR function ϕ (L tot) is fitted very well by a lognormal distribution over 5 decades of luminosity. We find that the bivariate luminosity function ϕ (L FUV, L FIR) shows a bimodal behavior, with L FIR tracking L FUV for L tot< 10 10 L☉ and L FUV saturating at~ 10 10 L☉, while L tot~ L FIR for higher luminosities. We also calculate the SFR density and compare it with other measurements.